Additional parameters used in this analysis are defined in Table~\ref{tab:symbol2}. 

\begin{table}[htbp]
%\begin{table}[t]
\small
\centering
%\tabcolsep=0.11cm
\begin{tabular}{|p{1.0cm}|p{5.75cm}|}
\hline
$k$ &  the number of top most popular chunks selected for deduplication\\ 
\hline
$c$ &  the total amount of data chunks in a cluster of VMs\\ 
\hline
$c_u$ &  the total amount of unique fingerprints after perfect  deduplication\\
\hline
$f_i$ &  the frequency for the $i$th most popular fingerprint\\
\hline
$\delta$ &  the percentage of duplicates detected in local deduplication\\
\hline
$\sigma$ & = percentage of unique data  belonging to  PDS\\
%\hline
%$V$ & the average number of VMs per machine\\
\hline
%$E_c, E_o$ & deduplication efficiency of VC and VO \\
%\hline
%$D$ & the amount of unique data on each machine\\
%\hline
%$s$ & the average data chunk size. Our setting is  4K.\\
%\hline
%$s$ & the average number of chunks per FSB\\
%\hline
%$m$ & memory size on each node used by VC\\ 
%\hline
%$E$ & the size of an popular data index entry\\
%\hline
%$N_1$, $N_2$ & the average no.  of non-PDS and PDS file blocks in a VM in VC\\
%\hline
%$N_o$, $V_o$ & the average no.  of file blocks  in a VM and the average no. of VMs shared by a file system block in VO\\
%\hline
%A(r) & availability of a file block with $r$ replicas and $d$ failed physical machines\\
\hline
\end{tabular}
\caption{Parameters for modeling deduplication with top $k$ popular chunks.}
\label{tab:symbol}
\end{table}


